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The homotopy type of algebraic cobordism categories

Presented by: 
Fabian Hebestreit
Wednesday 5th December 2018 - 11:30 to 12:30
INI Seminar Room 1
Co-authors: Baptiste Calmès (Université d'Artois), Emanuele Dotto (RFWU Bonn), Yonatan Harpaz (Université Paris 13), Markus Land (Universität Regensburg), Kristian Moi (KTH Stockholm), Denis Nardin (Université Paris 13), Thomas Nikolaus (WWU Münster), Wolfgang Steimle (Universität Augsburg). Abstract: I will introduce cobordism categories of Poincaré chain complexes, or more generally of Poincaré objects in any hermitian quasi-category C. One interest in such algebraic cobordism categories arises as they receive refinements of Ranicki's symmetric signature in the form of functors from geometric cobordism categories à la Galatius-Madsen-Tillmann-Weiss. I will focus, however, on a more algebraic direction. The cobordism category of C can be delooped by an iterated Q-construction, that is compatible with Bökstedt-Madsen's delooping of the geometric cobordism category. The resulting spectrum is a derived version of Grothendieck-Witt theory and I will explain how its homotopy type can be computed in terms of the K- and L-Theory of C.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons